Traveling waves in the modelling of aerosolised skin grafts

Denman et al. [P.K. Denman, D.L.S. McElwain, J. Norbury, Analysis of travelling waves associated with the modelling of aerosolised skin grafts, Bull. Math. Biol. 69 (2007) 495-523] proposed a novel model on the growth pattern of keratinocyte cell colonies that were sprayed on to a severe burn site to facilitate the healing process. They studied traveling wave solutions of the model by asymptotic analysis and obtained several qualitative properties. In this paper we establish the following result on the traveling waves: there exists a minimal speed such that the model has a unique biologically meaningful travelling wave solution for each speed and has no such a solution for any c<c_min.